The office referred to Section 2 of the Act, saying official information is only that held by a Minister of the Crown in his official capacity.
National leader Bill English said Ardern needed to release the "secret agreement", which "goes to the very heart of the formation of the new Government".
"It is unacceptable for the Prime Minister to claim it's not public information. It is and the public deserves to know how the new Coalition, and therefore the country, will be run," English said.
"This is not the openness and accountability promised by Jacinda Ardern and Winston Peters and enshrined in the public version of their Coalition agreement. It's certainly not them living up to their promise to 'strengthen New Zealand's democracy by increasing public participation, openness, and transparency around official information'."
The refusal to release the document comes as National attacks Labour over what it says is a lack of transparency over answers to written questions, with Labour accusing the Opposition of time-wasting tactics.
Opposition MPs can lodge written questions to ministers, with the answers then published online. Since Labour came to power National has lodged thousands, with many asking what meetings a minister held on a specific date.
National says it is doing so because Labour will not provide proper answers, but Labour's Leader of the House Chris Hipkins has labelled the questions the equivalent of Parliamentary spam mail.